Combination of Taguchi Method and Artificial Intelligence Techniques are used for the Optimal Design of Flat-plate Collectors._ Soteris Kalogirou

1. Combination of Taguchi Method and
Artificial Intelligence Techniques for the
Optimal Design of Flat-plate Collectors
Soteris Kalogirou
Archimedes Solar Energy Laboratory
Cyprus University of Technology
Limassol, Cyprus

2. Objective
 To use a genetic algorithm for:
 the design of a flat-plate collector and
 for the selection of the right materials for the construction of the
collector.
 The genetic algorithm is used to maximize the thermal
efficiency of the collector estimated by the collector
optical efficiency and the slope of the standard collector
performance curve (heat loss coefficient) by:
 Determine the optimum combination of:
 The collector tube material,
 The type of collector absorbing plate material,
 The number of collector riser tubes,
 The collector riser tube diameter,
 The type of absorber coating and
 The thickness of the bottom insulating material.

3. Innovation
 The use of an evolution strategy based on genetic
algorithms to determine the optimum solution.
 An Artificial Neural Network is used to predict the
collector thermal efficiency based on the parameters
presented.
 The number of training cases on which the thermal
efficiency depends were selected using the method of
Taguchi experiments:
 Three levels of six variables were used together with three levels
of available solar radiation intensity (Gt) and collector inlet minus
ambient temperature difference.

4. Collector Equations
 The useful energy collected from a collector can be
obtained from:
 where FR is the heat removal factor given by:
 F΄ is the collector efficiency factor which is calculated by
considering the temperature distribution between two pipes
of the collector absorber and by assuming that the
temperature gradient in the flow direction is negligible
 
u R t L i a
Q AF G ( ) U T T
 
   
 
p L
R
L p
mc U F'A
F 1 Exp
AU mc
 
 
 
   
 
 
 
 

5.  F΄ is given by:
 Factor F is the standard fin efficiency for straight
fins with rectangular profile, obtained from:
 where n is given by:
δ
  












fi
i
b
L
L
h
D
C
F
D
W
D
U
W
U
F

1
1
)
(
1
1
'
 
2
/
)
(
2
/
)
(
tanh
D
W
n
D
W
n
F




k
U
n L


6.  The collector efficiency is found by dividing Qu
by the incident radiation AGt:
 Therefore from this analysis is clear that the
collector thermal efficiency depends on the factors
mentioned earlier.
 Additionally, by plotting η against ΔΤ/Gt a
straight line is obtained with:
 slope equal to FRUL, called the heat loss coefficient and
 intercept on the y-axis, equal to FR(τα), called optical
efficiency.
i a
R R L
t
T T
F ( ) F U
G
 

     
 

7. Collection of data
 The magnitude of the parameters applied in this work is:
 The collector performance depends also on the solar
radiation intensity and the temperature difference between
the collector inlet and ambient temperature. For these
parameters again three levels of data were used:
Parameter Level 1 Level 2 Level 3
A. Collector tube material
B. Collector absorbing plate material
C. Number of collector riser tubes
D. Collector riser tube diameter
E. Type of absorber coating
F. Thickness of bottom insulation
Copper
Aluminum
8
3
Tinox
2.5
Stainless steel
Copper
11
4
Vacuum spattering
3.8
-
Stainless steel
14
5
Spray painting
5
Parameter Level 1 Level 2 Level 3
P. Solar radiation intensity (W/m2)
Q. Temperature difference [=Ti-Ta] (°C)
800
10
900
20
1000
30

8. Collection of data
 When a full-functional orthogonal array is
considered with the data shown in previous Tables
a total of 21x37 (4374) experiments are required to
cover all possible combinations.
 By using the method of Taguchi experiments
however, only 18 experiments are required as
shown in following Table.

9. Collection of data
 By using the method of Taguchi experiments, only 18
experiments are required:
 A total of 162 patterns were
collected from the these
combinations.
For each row of the vertical columns
(18 cases) they were 9 combinations
of the horizontal cases with
combinations of radiation and
temperature (18x9=162).
 All estimations were performed
using CoDePro (collector design
program) software.

10. ANN Training
 From a total of 162 patterns that were collected:
 130 were used for the training of the ANN
 32, selected randomly, were used to validate the training accuracy.
 The input parameters are the factors on which the collector
performance depends, listed in previous Tables.
 The output parameters are:
 The collector optical efficiency, FR(τα) (intercept on the y-axis of
the collector performance curve) and
 The heat loss coefficient, FRUL (slope of the collector performance
curve).
 Sample data are shown in next slide:

11. Sample of training data
Input parameters Output parameters
A B C D E F P Q FR(τα) FRUL
1
1
1
1
1
1
1
1
1
….
1
1
1
1
1
1
1
1
1
….
8
8
8
8
8
8
8
8
8
…
3
3
3
3
3
3
3
3
3
…
1
1
1
1
1
1
1
1
1
….
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
….
800
800
800
900
900
900
1000
1000
1000
…
10
20
30
10
20
30
10
20
30
…
0.7584
0.7586
0.7595
0.7578
0.7581
0.7589
0.7572
0.7576
0.7383
…..
4.679
4.658
4.636
4.677
4.660
4.638
4.678
4.661
4.639
….
Note that numbers are used to differentiate the different inputs for parameters A,
B, D and E, whereas for the other parameters actual input data were used.

12. Artificial neural network architecture

13. Training accuracy
 Evaluated with the unknown data set.
 Correlation coefficients equal to 0.9914 and
0.9886 for the two parameters respectively
 Very satisfactory as they are very close to unity.
 The results also show that 94% of the data are
within 5% error, which is also very satisfactory.
 As this accuracy is based to a large extent on the
data used to train the ANN, the selection of the
training data with the Taguchi method seems to be
very effective.

14. Genetic Algorithms
 The genetic algorithm (GA) is a model of machine
learning, which derives its behavior from a representation
of the processes of evolution in nature – survival of the
fittest.
 Genetic algorithms (GA) are suitable for finding the
optimum solution in problems were a fitness function is
present.
 Genetic algorithms use a “fitness” measure to determine
which of the individuals in the population survive and
reproduce.
 Thus, survival of the fittest causes good solutions to progress.
 In this case, the genetic algorithm is seeking to breed an individual
that maximizes the collector efficiency.
 GAs implement crossover, mutation and other operations
on the data.

15. Genetic Algorithm Settings
 Population size=50
 Population size is the size of the genetic breeding pool
small value = not enough different kinds of individuals to solve the
problem satisfactorily.
Large value = good solution will take longer to be found.
 Crossover rate=90%
 Crossover rate determines the probability that the crossover
operator will be applied to a particular chromosome during a
generation.
 Mutation rate=1%
 Mutation rate determines the probability that the mutation operator
will be applied to a particular chromosome during a generation.
 Generation gap=96%
 Generation gap determines the fraction of those individuals that do
not go into the next generation.

16. Estimation Method
 For a combination of input parameters the ANN
predicts the two performance parameters:
 Optical efficiency
 Heat loss coefficient
 From these the collector efficiency is obtained.
 Subsequently a GA is used to try various
combinations, and based on the principles of
genetics, to find the combination of the input
parameters that maximize the collector efficiency.

17. Results
 The optimum combination of parameters obtained from the
GA are:
 These parameters result in an optimum efficiency that
depends on the magnitude of the solar radiation available.
 For the three values of solar radiation considered the results
are:
Parameter Value
A. Collector tube material
B. Collector absorbing plate material
C. Number of collector riser tubes
D. Collector riser tube diameter
E. Type of absorber coating
F. Thickness of bottom insulation
Copper
Copper
11
9mm
Tinox
50mm
Solar radiation (W/m2) Efficiency
800
900
1000
0.7536
0.7581
0.7614

18. Conclusions
 For each run of the program the optimum solution was
reached in less than 5 seconds on a Pentium 3.2 GHz
machine, which is very fast.
 It is proved that this way of selecting the variety of training
parameters with the Taguchi method is very effective in
allowing the ANN to learn the behavior of the system
satisfactorily.
 To find the optimum parameters a genetic algorithm is
used.
 The results obtained are very similar to the results obtained
by other researchers using much complicated optimization
methods, like the grey relational analysis, whereas the
present method not only is very accurate but it is also very
quick.

19. Archimedes Solar Energy Laboratory

20. Thank you for your attention….
Any questions please….
Email: soteris.kalogirou@cut.ac.cy